Introduction. Figure $2\mathrm{.}1$ below shows a composite cross section fabricated by welding a structural T to the sidewall of a hollow square tube. The structural T and the square tube have uniform and equivalent thickness $\backslash ($ t $\backslash )$; they also have similar material properties.

Problem.

a$)$ Assuming $\backslash (\backslash$boldsymbol$\{$b$\}\backslash$gg $\backslash$boldsymbol$\{$t$\}\backslash ),$ develop expressions for the torsional moment resisted by each element in Figure $2\mathrm{.}1$ caused by an applied torque $\backslash (\backslash$boldsymbol$\{$M$\}\_\{\backslash$boldsymbol$\{$x$\}\}\backslash )$ of $10$ ft $-$kips. Assume that warping is not restrained.

b$)$ As an alternative design, consider the rectangular tube section shown in Figure $2\mathrm{.}2.$ Develop an expression for its width $\backslash (\backslash$boldsymbol$\{$W$\}\backslash )$ so that the torsional stiffness of the rectangular tube in Figure $2\mathrm{.}2$ is equivalent to that for the composite section shown in Figure $2\mathrm{.}1.$

c$)$ Discuss the implications of your results for part b as the aspect ratio $\backslash ($ b $/$ t $\backslash$rightarrow $\backslash$infty $\backslash ).$

Figure $2\mathrm{.}1$ Composite Cross Section. send me the answer on a paper